1. Field of the Invention
The present invention relates to a multifrequency filter bank, and more particularly to a method of designing a subband filter bank.
2. Description of the Related Art
A filter bank is a group of filters used for passing various frequency bands. A number of filters may exist for each frequency band. Subband filter banks have diverse applications in audio and video data compression.
FIG. 1 is a block diagram of a 2-band filter bank. The 2-band filter bank comprises a receiving section 10, transmission section 20, and sending section 30. The receiving section includes first and second analysis filters 12 and 14 and first and second decimators 16 and 18. The sending section 30 includes first and second expanders 32 and 34, first and second synthesis filters 36 and 38, and an adder/subtractor 40. Here, H0(Z), H1(Z), G0(Z), and G1(Z) are transfer functions of the corresponding filters.
According to the subband filter bank of FIG. 1, the decimators 16 and 18 are connected to the output of the analysis filter 12 and 14, respectively. The decimators 16 and 18 may alternatively be connected to the inputs of the analysis filters 12 and 14 in other multirate filter banks.
The first and second analysis filters 12 and 14 receive a digital signal x(n), filter predetermined frequency bands and output a filtered digital signal x'(n)! to the first and second decimators 16 and 18, respectively. The first and second decimators 16 and 18 filter components whose indexes are even-numbered and output the filtered components to the transmission section 20.
The first and second expander 32 and 34 interpolate `0` into the digital signal of the even-numbered components, for example, x'(0), x'(2), etc., from the transmission section 20. The interpolated signal is output to the corresponding synthesis filter 36 or 38. The reason why the expander 32 or 34 interpolates `0` between x'(0) and x'(2) is to match the Nyquist sampling rate. The adder/subtractor section 40 adds or subtracts the digital signal interpolated through the synthesis filters 36 and 38 and produces an output signal y(n) in which the input signal x(n) is delayed for a predetermined time r, that is, y(n)=x(n-r).
A conventional method of designing a filter bank which has a 2-band liner phase (LP) and satisfies a perfect reconstruction (PR) condition involves first designing, the first and second analysis filters 12 and 14. The synthesis filters are then designed corresponding to the designed analysis filters 12 and 14. Since complex operations such as solving non-linear equations are required, it is almost impossible to design the filters using a system with limited processing capacity such as a personal computer.